This text is an extension of notes from courses first given during the 1990-ies for engineers employed in industry, and then for master students in the international masters programme at Chalmers Technical University in Gothenburg 2001-2009. Hence, it covers most issues of fatigue analysis as taught on the master level in universities. The micromechanical features of fatigue as studied in materials science constitute an area of research and education in itself. The descriptions here are simplistic. Some fundamental models are introduced just to give qualitative indications of the micromechanical background to fatigue phenomena. These models are useful for the understanding of principal effects found by experiments on the macroscopic level. Some emphasis is given to the stochastic nature of fatigue. The use of statistical methods in design is described as well as uncertainty assessments in the evaluation of experiments to find material properties connected to fatigue. Most of the mathematical expressions used in fatigue design are not physical laws but suitable models suggested from curve fitting of experimental results, and then a critical statistical assessment is essential. The aim is to supply an easy-to-use support to people working with fatigue in industrial environments or as teachers on the bachelor or master level in universities. It should give useful background and understanding to handbook formulas and requirements in standards. If the text is used in courses it should be complemented by examples and problems to solve since only a few examples of a principal character are included. Likewise, extensive handbook data for e g stress concentration and stress intensity factors, and material properties, are necessary for use in practical design situations. Computer programs for solving of various problems, as FEM codes or procedures to find load spectra are not included, since the field is changing quickly, and the Internet gives ample information. The intention has not been to produce a reference work for scientific studies of fatigue. Therefore, literature references are few and only including works of authors having produced milestone contributions to the area, or well renowned textbooks, standards, and handbooks. It is underlined that all experimental evidence shows that fatigue phenomena in real materials can by no means be precisely described by mathematical models and formulas. Models are sometimes developed in the text by sophisticated mathematical tools giving such an impression. But they are just models, often competing with one another, and they only constitute a framework for understanding and approximate data for design.